Choosability with separation of complete multipartite graphs and hypergraphs

Details Choosability with separation of complete multipartite graphs and hypergraphs Choosability with separation of complete multipartite graphs and hypergraphs

2011-09-14

arxiv.org/abs/1109.2969v1

Mathematics

Combinatorics

9 pages

Scientific paper

For a hypergraph G and a positive integer s, let \chi_{\ell} (G,s) be the minimum value of l such that G is L-colorable from every list L with |L(v)|=l for each v\in V(G) and |L(u)\cap L(v)|\leq s for all u, v\in e\in E(G). This parameter was studied by Kratochv\'{i}l, Tuza and Voigt for various kinds of graphs. Using randomized constructions we find the asymptotics of \chi_{\ell} (G,s) for balanced complete multipartite graphs and for complete k-partite k-uniform hypergraphs.

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